R  Programming is free software tools

R is free software and comes with 

Yes,R programming language is free software to use data analytics,data science etc

You are welcome to redistribute it under certain conditions.

Type 'license()' or 'licence()' for distribution details.

R code


R is a collaborative project with many contributors.

Type 'contributors()' for more information and

'citation()' on how to cite R or R packages in publications.

R  Programming is free software tools.We learn to write code.

> library("Deriv", lib.loc="~/R/win-library/3.6")

This is R version 3.6.3 

> D(expression(2*xˆ3),"x")

How do you write log with  R

> D(expression(log(x)),"x")

1/x

> D(expression(a*exp(-b * x)),"x")

-(a * (exp(-b * x) * b))

> D(expression(a/(1+b*exp(-c * x))),"x")

a * (b * (exp(-c * x) * c))/(1 + b * exp(-c * x))^2

> trig.exp <- expression(sin(cos(x + yˆ2)))

How do you write  sin, cos identites  with R.

> trig.exp <- expression(sin(cos(x + y^2)))

> D(trig.exp,"x")

-(cos(cos(x + y^2)) * sin(x + y^2))

> D(expression(2*x^3),"x")

2 * (3 * x^2)

> library("deSolve", lib.loc="~/R/win-library/3.6")

> x <- seq(0,10,0.1)

> x

  [1]  0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0

 [12]  1.1  1.2  1.3  1.4  1.5  1.6  1.7  1.8  1.9  2.0  2.1

 [23]  2.2  2.3  2.4  2.5  2.6  2.7  2.8  2.9  3.0  3.1  3.2

 [34]  3.3  3.4  3.5  3.6  3.7  3.8  3.9  4.0  4.1  4.2  4.3

 [45]  4.4  4.5  4.6  4.7  4.8  4.9  5.0  5.1  5.2  5.3  5.4

 [56]  5.5  5.6  5.7  5.8  5.9  6.0  6.1  6.2  6.3  6.4  6.5

 [67]  6.6  6.7  6.8  6.9  7.0  7.1  7.2  7.3  7.4  7.5  7.6

 [78]  7.7  7.8  7.9  8.0  8.1  8.2  8.3  8.4  8.5  8.6  8.7

 [89]  8.8  8.9  9.0  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8

[100]  9.9 10.0

How do you write  expoential equation in R.

> y1 <- 2+5*x-0.2*x^2

> y1

  [1]  2.000  2.498  2.992  3.482  3.968  4.450  4.928

  [8]  5.402  5.872  6.338  6.800  7.258  7.712  8.162

 [15]  8.608  9.050  9.488  9.922 10.352 10.778 11.200

 [22] 11.618 12.032 12.442 12.848 13.250 13.648 14.042

 [29] 14.432 14.818 15.200 15.578 15.952 16.322 16.688

 [36] 17.050 17.408 17.762 18.112 18.458 18.800 19.138

 [43] 19.472 19.802 20.128 20.450 20.768 21.082 21.392

 [50] 21.698 22.000 22.298 22.592 22.882 23.168 23.450

 [57] 23.728 24.002 24.272 24.538 24.800 25.058 25.312

 [64] 25.562 25.808 26.050 26.288 26.522 26.752 26.978

 [71] 27.200 27.418 27.632 27.842 28.048 28.250 28.448

 [78] 28.642 28.832 29.018 29.200 29.378 29.552 29.722

 [85] 29.888 30.050 30.208 30.362 30.512 30.658 30.800

 [92] 30.938 31.072 31.202 31.328 31.450 31.568 31.682

 [99] 31.792 31.898 32.000

> y2<- 2+5*x-0.4*x^2

> y2

  [1]  2.000  2.496  2.984  3.464  3.936  4.400  4.856

  [8]  5.304  5.744  6.176  6.600  7.016  7.424  7.824

 [15]  8.216  8.600  8.976  9.344  9.704 10.056 10.400

 [22] 10.736 11.064 11.384 11.696 12.000 12.296 12.584

 [29] 12.864 13.136 13.400 13.656 13.904 14.144 14.376

 [36] 14.600 14.816 15.024 15.224 15.416 15.600 15.776

 [43] 15.944 16.104 16.256 16.400 16.536 16.664 16.784

 [50] 16.896 17.000 17.096 17.184 17.264 17.336 17.400

 [57] 17.456 17.504 17.544 17.576 17.600 17.616 17.624

 [64] 17.624 17.616 17.600 17.576 17.544 17.504 17.456

 [71] 17.400 17.336 17.264 17.184 17.096 17.000 16.896

 [78] 16.784 16.664 16.536 16.400 16.256 16.104 15.944

 [85] 15.776 15.600 15.416 15.224 15.024 14.816 14.600

 [92] 14.376 14.144 13.904 13.656 13.400 13.136 12.864

 [99] 12.584 12.296 12.000

> y3 <- 2+4*x-0.6*xˆ2+0.04*xˆ3

Error: unexpected input in "y3 <- 2+4*x-0.6*xˆ"

> y3 <- 2+4*x-0.6*x^2+0.04*x^3

> plot(y3)

> plot(y2)

> y4 <- 2+4*x+2*x^2-0.6*x^3+0.04*x^4

> plot(y4)

> par(mfrow=c(2,2))

> plot(x,y1,type="l",ylab="y",main="decelerating")

> plot(x,y2,type="l",ylab="y",main="humped")

> plot(x,y3,type="l",ylab="y",main="inflection")

> plot(x,y4,type="l",ylab="y",main="local maximum")

> par(mfrow=c(2,2))

> y1 <- x/(2+5*x)

> y2 <- 1/(x-2+4/x)

> y3 <- 1/(xˆ2-2+4/x)

Error: unexpected input in "y3 <- 1/(xˆ"

> y3 <- 1/(x^2-2+4/x)

> plot(x,y1,type="l",ylab="y",main="Michaelis-Menten")

> plot(x,y2,type="l",ylab="y",main="shallow hump")

> plot(x,y3,type="t",ylab="y",main="steep hump")

Error in plot.xy(xy, type, ...) : invalid plot type 't'

> plot(x,y3,type="l",ylab="y",main="steep hump")

> #Gamma function

> par(mfrow=c(1,1))

> t <- seq(0.2,4,0.01)

> t

  [1] 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30

 [12] 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41

 [23] 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52

 [34] 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63

 [45] 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74

 [56] 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85

 [67] 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96

 [78] 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07

 [89] 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18

[100] 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29

[111] 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40

[122] 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51

[133] 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62

[144] 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73

[155] 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84

[166] 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95

[177] 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06

[188] 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17

[199] 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28

[210] 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39

[221] 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

[232] 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61

[243] 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72

[254] 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83

[265] 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94

[276] 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05

[287] 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16

[298] 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27

[309] 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38

[320] 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49

[331] 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.60

[342] 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71

[353] 3.72 3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.80 3.81 3.82

[364] 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.90 3.91 3.92 3.93

[375] 3.94 3.95 3.96 3.97 3.98 3.99 4.00

> plot(t,gamma(t),type="l")

> abline(h=1,lty=2)

> par(mfrow=c(2,2))

> x <- seq(0,10,0.1)

> plot(x,y,type="l",main="three-parameter logistic")

Error in xy.coords(x, y, xlabel, ylabel, log) : object 'y' not found

> y <- 100/(1+90*exp(-1*x))

> plot(x,y,type="l",main="three-parameter logistic")

> y <- 20+100/(1+exp(0.8*(3-x)))

> plot(x,y,ylim=c(0,140),type="l",main="four-parameter logistic")

> x <- -200:100

> y <- 100*exp(-exp(0.02*x))

> plot(x,y,type="l",main="negative Gompertz")

> x <- 0:100

> y <- 50*exp(-5*exp(-0.08*x))

> plot(x,y,type="l",main="positive Gompertz")

> #Biexponential model

> a <- 10

> b <- -0.8

> c <- 10

> d <- -0.05

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ - + -",type="l")

> a <- 10

> b <- -0.8

> c <- 10

> d <- 0.05

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ - + +",type="l")

> a <- 200

> b <- 0.2

> c <- -1

> d <- 0.7

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ + - +",type="l")

> a <- 200

> b <- 0.05

> c <- 300

> d <- -0.5

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ + + -",type="l")

> par(mfrow=c(1,1))

> x <- 0:6

> plot(x,factorial(x),type="s",main="factorial x",log="y")

> choose(8,3)

[1] 56

> plot(0:8,choose(8,0:8),type="s",main="binomial coefficients")

> curve(pnorm(x),-3,3)

> arrows(-1,0,-1,pnorm(-1),col="red")

> arrows(-1,pnorm(-1),-3,pnorm(-1),col="green")

> pnorm(-1)

[1] 0.1586553

> curve(dnorm(x),-3,3)

> par(mfrow=c(2,2))

> x <- seq(-3,3,0.01)

> y <- exp(-abs(x))

> plot(x,y,type="l",main= "x")

> y <- exp(-abs(x)ˆ3)

Error: unexpected input in "y <- exp(-abs(x)ˆ"

> y <- exp(-abs(x)^3)

> plot(x,y,type="l",main= "x")

> y <- exp(-abs(x)^8)

> plot(x,y,type="l",main= "x")

> y <- exp(-abs(x)^21)

> plot(x,y,type="l",main= "x")

> x <- seq(-3,3,0.01)

> z <- seq(-3,-1.25,0.01)

> p <- dnorm(z)

> z <- c(z,-1.25,-3)

> p <- c(p,min(p),min(p))

> plot(x,dnorm(x),type="l",xaxt="n",ylab="probability density",xlab="height")

> axis(1,at=-3:3,labels=c("146","154","162","170","178","186","192"))

> polygon(z,p,col="red")

> z <- seq(1.875,3,0.01)

> p <- dnorm(z)

> z <- c(z,3,1.875)

> p <- c(p,min(p),min(p))

> plot(x,dnorm(x),type="l",xaxt="n",ylab="probability density",xlab="height")

> axis(1,at=-3:3,labels=c("146","154","162","170","178","186","192"))

> polygon(z,p,col="red")

> z <- seq(-0.635,1.25,0.01)

> p <- dnorm(z)

> z <- c(z,1.25,-0.635)

> p <- c(p,0,0)

> plot(x,dnorm(x),type="l",xaxt="n",ylab="probability density",xlab="height")

> axis(1,at=-3:3,labels=c("146","154","162","170","178","186","192"))

> polygon(z,p,col="red")

> #The central limit theorem

> par(mfrow=c(1,1))

> hist(runif(10000)*10,main="")

> means <- numeric(10000)

> for (i in 1:10000){

+     means[i] <- mean(runif(5)*10)

+ }

> hist(means,ylim=c(0,1600),main="")

> mean(means)

[1] 4.990829

> sd(means)

[1] 1.293516

> xv <- seq(0,10,0.1)

> yv <- dnorm(xv,mean=4.998581,sd=1.28996)*5000

> lines(xv,yv)

> par(mfrow=c(2,2))

> hist(sample(1:6,replace=T,10000),breaks=0.5:6.5,main="",xlab="one die")

> a <- sample(1:6,replace=T,10000)

> b <- sample(1:6,replace=T,10000)

> hist(a+b,breaks=1.5:12.5,main="", xlab="two dice")

> c <- sample(1:6,replace=T,10000)

> hist(a+b+c,breaks=2.5:18.5,main="", xlab="three dice")

> d <- sample(1:6,replace=T,10000)

> e <- sample(1:6,replace=T,10000)

> hist(a+b+c+d+e,breaks=4.5:30.5,main="", xlab="five dice")

> mean(a+b+c+d+e)

[1] 17.5012

> sd(a+b+c+d+e)

[1] 3.819877

> lines(seq(1,30,0.1),dnorm(seq(1,30,0.1),17.5937,3.837668)*10000)

> #Maximum likelihood with the normal distribution

> par(mfrow=c(2,2))

> curve(dnorm,-3,3,xlab="z",ylab="Probability density",main="Density")

> curve(pnorm,-3,3,xlab="z",ylab="Probability",main="Probability")

> curve(qnorm,0,1,xlab="p",ylab="Quantile (z)",main="Quantiles")

> y <- rnorm(1000)

> hist(y,xlab="z",ylab="frequency",main="Random numbers")

> yvals <- rnorm(100,24,4)

> mean(yvals)

[1] 23.98589

> sd(yvals)

[1] 3.395763

> ydevs <- rnorm(100,0,1)

> ydevs <- (ydevs-mean(ydevs))/sd(ydevs)

> mean(ydevs)

[1] -1.587923e-17

> sd(ydevs)

[1] 1

> yvals <- 24 + ydevs*4

> mean(yvals)

[1] 24

> sd(yvals)

[1] 4

> windows(7,4)

> par(mfrow=c(1,2))

> x <- seq(0,30,.25)

> plot(x,pchisq(x,3,7.25),type="l",ylab="p(x)",xlab="x")

> plot(x,pchisq(x,5,10),type="l",ylab="p(x)",xlab="x")

> 8*10.2/qchisq(.975,8)

[1] 4.65367

> 8*10.2/qchisq(.025,8)

[1] 37.43582

> qf(.95,2,18)

[1] 3.554557

> x <- seq(0.05,4,0.05)

> plot(x,df(x,2,18),type="l",ylab="f(x)",xlab="x")

> plot(x,df(x,6,18),type="l",ylab="f(x)",xlab="x")

> windows(7,7)

> par(mfrow=c(1,1))

> df <- seq(1,30,.1)

> plot(df,qf(.95,df,30),type="l",ylab="Critical F")

> lines(df,qf(.95,df,10),lty=2)

> x <- seq(0.01,3,0.01)

> plot(x,df(x,1,10),type="l",ylim=c(0,1),ylab="f(x)")

> lines(x,df(x,2,10),lty=6,col="red")

> lines(x,df(x,5,10),lty=2,col="green")

> lines(x,df(x,30,10),lty=3,col="blue")

> legend(2,0.9,c("1","2","5","30"),col=(1:4),lty=c(1,6,2,3),

+        title="numerator d.f.")

> curve( (1+xˆ2)ˆ(-0.5), -3, 3,ylab="t(x)",col="red")

Error: unexpected input in "curve( (1+xˆ"

> curve( (1+x^2)^(-0.5), -3, 3,ylab="t(x)",col="red")

> plot(1:30,qt(0.975,1:30), ylim=c(0,12),type="l",

+      ylab="Students t value",xlab="d.f.",col="red")

> abline(h=2,lty=2,col="green")

> xvs <- seq(-4,4,0.01)

> plot(xvs,dnorm(xvs),type="l",lty=2,

+     ylab="Probability density",xlab="Deviates")

> lines(xvs,dt(xvs,df=5),col="red")

> qt(0.975,5)

[1] 2.570582

> #The gamma distribution

> x <- seq(0.01,4,.01)

> par(mfrow=c(2,2))

> y <- dgamma(x,.5,.5)

> plot(x,y,type="l",col="red",main="alpha = 0.5")

> y <- dgamma(x,.8,.8)

> plot(x,y,type="l",col="red", main="alpha = 0.8")

> x <- seq(0,1,0.01)

> fx <- dbeta(x,2,3)

> plot(x,fx,type="l",main="a=2 b=3",col="red")

> fx <- dbeta(x,0.5,2)

> plot(x,fx,type="l",main="a=0.5 b=2",col="red")

> fx <- dbeta(x,2,0.5)

> plot(x,fx,type="l",main="a=2 b=0.5",col="red")

> fx <- dbeta(x,0.5,0.5)

> plot(x,fx,type="l",main="a=0.5 b=0.5",col="red")

> rbeta(10,2,3)

 [1] 0.10678527 0.46414831 0.09402682 0.74723789 0.43859319

 [6] 0.49928575 0.83196791 0.13017362 0.17905408 0.61618885

> windows(7,4)

> par(mfrow=c(1,2))

> plot(-200:200,dcauchy(-200:200,0,10),type="l",ylab="p(x)",xlab="x",

+      col="red")

> plot(-200:200,dcauchy(-200:200,0,50),type="l",ylab="p(x)",xlab="x",

+      col="red")

> windows(7,7)

> plot(seq(0,10,0.05),dlnorm(seq(0,10,0.05)),

+      type="l",xlab="x",ylab="LogNormal f(x)",col="x")

Error in plot.xy(xy, type, ...) : invalid color name 'x'

> plot(seq(0,10,0.05),dlnorm(seq(0,10,0.05)),

+ type="l",xlab="x",ylab="LogNormal f(x)",col="x")

Error in plot.xy(xy, type, ...) : invalid color name 'x'

> windows(7,7)

> a <- 3

> l <- 1

> t <- seq(0,1.8,.05)

> ft <- a*l*tˆ(a-1)*exp(-l*tˆa)

Error: unexpected input in "ft <- a*l*tˆ"

> ft <- a*l*t^(a-1)*exp(-l*t^a)

> plot(t,ft,type="l",col="blue",ylab="f(t) ")

> a <- 1

> ft <- a*l*t^(a-1)*exp(-l*t^a)

> lines(t,ft,type="l",col="red")

> a <- 2

> ft <- a*l*t^(a-1)*exp(-l*t^a)

> lines(t,ft,type="l",col="green")

> legend(1.4,1.1,c("1","2","3"),title="alpha",lty=c(1,1,1),col=c(2,3,4))

> xy <- mvrnorm(1000,mu=c(50,60),matrix(c(4,3.7,3.7,9),2))

Error in mvrnorm(1000, mu = c(50, 60), matrix(c(4, 3.7, 3.7, 9), 2)) : 

  could not find function "mvrnorm"

> x <- ceiling(runif(10000)*6)

> table(x)

x

   1    2    3    4    5    6 

1702 1693 1639 1684 1591 1691 

> hist(x,breaks=0.5:6.5,main="")

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